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Which is a factor?

Which of the following is a factor of 5x2+7x-6? 
 
A. X-1 
B. X-2 
C. 5x+3 
D. 5x-3

3 Answers by Expert Tutors

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Jack J. | Experienced and Friendly Tutor from Johns HopkinsExperienced and Friendly Tutor from John...
5.0 5.0 (4 lesson ratings) (4)
1
Check Marked as Best Answer
Let’s set up the factors, with A and B being our unknown numbers:
5x2+7x-6 = 
(5x+A)*(x+B)

Expand and Simplify:
(5x+A)*(x+B) = 5x2 + 5Bx + Ax + AB
= 5x2 + (5B+A)x + AB

From here we can set up the comparisons:
5x+ 7x - 6 = 5x2 + (5B+A)x + AB

7 = (5B+A)
-6 = AB

Let’s start with -6 = AB and find what product pairs work:
(1 and -6), (-1 and 6), (2 and -3), (-2 and 3), (3 and -2), (-3 and 2), (6 and -1), or (-6 and 1).

Now we plug in our (A and B) pairs above to see which one works for our other equation:
7 = (5B+A) = (A+5B)

For (1 and -6): 1 + 5(-6) = -29; no.
For (-1 and 6): -1 + 5(6) = 29; no.
.
.
.
For (-3 and 2): -3 +5(2) = 7; yes!


Plug the correct pair back into (5x+A)*(x+B)
(5x-3)*(x+2)
 
Final Answer: D
Elias A. | Experienced how to help studentsExperienced how to help students
0
5x2 + 7x-6
5x2 +10x-3x-6
5x(x+2)-3(x+2)
(5x-3)(x+2)

Therefore, the answer is D

Mark M. | Mathematics Teacher - NCLB Highly QualifiedMathematics Teacher - NCLB Highly Qualif...
4.9 4.9 (159 lesson ratings) (159)
-1
5x2 + 7x - 6
(5x - 3)(x + 2)